Put the mushrooms in a bowl and pour the boiling water over them. Let soak until tender, 20 to 25 minutes. Lift the mushrooms from the water, leaving any grit at the bottom of the bowl. Pat the mushrooms dry with a kitchen towel, discard the stems and thinly slice the caps. Strain the mushroom soaking liquid through a fine sieve and reserve it in a small bowl.
Sprinkle the chicken thighs liberally with salt and pepper. Heat the oil in a large high-sided skillet over medium-high heat until it shimmers. Sear the chicken thighs on both sides until golden brown, 5 to 6 minutes total. (You may need to do this in 2 batches to avoid crowding the skillet.) Transfer the browned chicken thighs to a rimmed baking sheet and bake in the oven until the internal temperature of the chicken reaches 160 degrees F, 12 to 15 minutes.
In the same pan that you seared the chicken thighs, saute the garlic, ginger, onions and sliced mushrooms over medium heat until the onions are soft, 6 to 8 minutes. Stir in the miso paste and cook for 2 minutes. Add the chicken broth and reserved mushroom liquid. Bring to a boil, then reduce the heat to a simmer and cook for 10 minutes.
Meanwhile, soak the noodles in a bowl of hot water until soft, 3 to 5 minutes. Drain.
To serve, put 1/2 cup glass noodles in each serving bowl. Top with the bok choy, chicken and miso broth.
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